1

Multiple sequence alignment and phylogenetic trees

Stat 246, Spring 2002, Week 5b

2

A version of the “tree of life”

Obtained from aligned sequences of ribosomal RNA

3

Species trees and gene trees(after M. Nei 1987, Molecular Evolutionary Genetics.)

A A A

B B B

X Y Z X Y Z X Y Z

TimeGenes can be polymorphic before speciation, in different ways.

4

Tree topology

A E C D B F A E D C B F

A E C D B F F B D C E A

Identical:

Notidentical:

5

Tree reconstruction

A B C B A C C A B

6

Tree reconstruction (2)

A C B D B C A D C D A B D C A B

A B C D B A C D C B A D D B C A

A D C B B D C A C A B D D A B C

A B C D

A C B D

A D B C

7

Tree reconstruction (3)

• In general, for any strictly bifurcating rooted tree with n species, there are

different topologies.

n #trees 5 105 15 213,458,046,676,875 20 8,200,794,532,637,891,559,375

For unrooted trees, it’s only

€

2n−3( )!2n−2 n−2( )!( )

€

2n−5( )!2n−3 n−3( )!( )

8

Tree reconstruction (4)

• Distance-based methods UPGMA Transformed distance Neighbors relation Neighbor-joining

• Character state-based methods Maximum parsimony Linear invariants

• Maximum Likelihood

9

Beta-globins (orthologues)10 20 30 40

M V H L T P E E K S A V T A L W G K V N V D E V G G E A L G R L L V V Y P W T Q BG-human- . . . . . . . . N . . . T . . . . . . . . . . . . . . . . . . . . . . . . . . BG-macaque

- - M . . A . . . A . . . . F . . . . K . . . . . . . . . . . . . . . . . . . . BG-bovine- . . . S G G . . . . . . N . . . . . . I N . L . . . . . . . . . . . . . . . . BG-platypus

. . . W . A . . . Q L I . G . . . . . . . A . C . A . . . A . . . I . . . . . . BG-chicken- . . W S E V . L H E I . T T . K S I D K H S L . A K . . A . M F I . . . . . T BG-shark

50 60 70 80

R F F E S F G D L S T P D A V M G N P K V K A H G K K V L G A F S D G L A H L D BG-human. . . . . . . . . . S . . . . . . . . . . . . . . . . . . . . . . . . . N . . . BG-macaque

. . . . . . . . . . . A . . . . N . . . . . . . . . . . . D S . . N . M K . . . BG-bovine. . . . A . . . . . S A G . . . . . . . . . . . . A . . . T S . G . A . K N . . BG-platypus

. . . A . . . N . . S . T . I L . . . M . R . . . . . . . T S . G . A V K N . . BG-chicken. Y . G N L K E F T A C S Y G - - - - - . . E . A . . . T . . L G V A V T . . G BG-shark

90 100 110 120

N L K G T F A T L S E L H C D K L H V D P E N F R L L G N V L V C V L A H H F G BG-human. . . . . . . Q . . . . . . . . . . . . . . . . K . . . . . . . . . . . . . . . BG-macaque

D . . . . . . A . . . . . . . . . . . . . . . . K . . . . . . . V . . . R N . . BG-bovineD . . . . . . K . . . . . . . . . . . . . . . . N R . . . . . I V . . . R . . S BG-platypus. I . N . . S Q . . . . . . . . . . . . . . . . . . . . D I . I I . . . A . . S BG-chicken

D V . S Q . T D . . K K . A E E . . . . V . S . K . . A K C F . V E . G I L L K BG-shark

130 140

K E F T P P V Q A A Y Q K V V A G V A N A L A H K Y HBG-human. . . . . Q . . . . . . . . . . . . . . . . . . . . .BG-macaque

. . . . . V L . . D F . . . . . . . . . . . . . R . .BG-bovine. D . S . E . . . . W . . L . S . . . H . . G . . . .BG-platypus. D . . . E C . . . W . . L . R V . . H . . . R . . .BG-chicken

D K . A . Q T . . I W E . Y F G V . V D . I S K E . . BG-shark

. means same as reference sequence

- means deletion

10

Beta-globins: Uncorrected pairwise distances

Distances: between protein sequences. Calculated over: 1 to 147 Below diagonal: observed number of differences Above diagonal: number of differences per 100 amino acids

hum mac bov pla chi sha

hum ---- 5 16 23 31 65 mac 7 ---- 17 23 30 62 bov 23 24 ---- 27 37 65

pla 34 34 39 ---- 29 64

chi 45 44 52 42 ---- 61 sha 91 88 91 90 87 ----

11

Beta-globins: Corrected pairwise distances

Distances: between protein sequences. Calculated over: residues 1 to 147 Below diagonal: observed number of differences Above diagonal: estimated number of substitutions per 100 amino acids Correction method: Jukes-Cantor (see Von Bing’s lecture)

hum mac bov pla chi sha

hum ---- 5 17 27 37 108 mac 7 ---- 18 27 36 102 bov 23 24 ---- 32 46 110

pla 34 34 39 ---- 34 106

chi 45 44 52 42 ---- 98 sha 91 88 91 90 87 ----

12

UPGMA tree

BG-bovine

BG-humanBG-macaque

BG-platypus

BG-chicken

BG-shark

13

UPGMA tree (alternate form)BG-shark

BG-chicken

BG-platypus

BG-bovine

BG-human

BG-macaque

14

Human globins(paralogues)

10 20 30

- V L S P A D K T N V K A A W G K V G A H A G E Y G A E A L E R M F L S F P T T alpha-humanV H . T . E E . S A . T . L . . . . - - N V D . V . G . . . G . L L V V Y . W . beta-humanV H . T . E E . . A . N . L . . . . - - N V D A V . G . . . G . L L V V Y . W . delta-human

V H F T A E E . A A . T S L . S . M - - N V E . A . G . . . G . L L V V Y . W . epsilon-humanG H F T E E . . A T I T S L . . . . - - N V E D A . G . T . G . L L V V Y . W . gamma-human- G . . D G E W Q L . L N V . . . . E . D I P G H . Q . V . I . L . K G H . E . myo-human

40 50 60 70

K T Y F P H F - D L S H G S A - - - - - Q V K G H G K K V A D A L T N A V A H V alpha-humanQ R F . E S . G . . . T P D . V M G N P K . . A . . . . . L G . F S D G L . . L beta-humanQ R F . E S . G . . . S P D . V M G N P K . . A . . . . . L G . F S D G L . . L delta-humanQ R F . D S . G N . . S P . . I L G N P K . . A . . . . . L T S F G D . I K N M epsilon-humanQ R F . D S . G N . . S A . . I M G N P K . . A . . . . . L T S . G D . I K . L gamma-human

L E K . D K . K H . K S E D E M K A S E D L . K . . A T . L T . . G G I L K K K myo-human

80 90 100 110

D D M P N A L S A L S D L H A H K L R V D P V N F K L L S H C L L V T L A A H L alpha-human. N L K G T F A T . . E . . C D . . H . . . E . . R . . G N V . V C V . . H . F beta-human. N L K G T F . Q . . E . . C D . . H . . . E . . R . . G N V . V C V . . R N F delta-human

. N L K P . F A K . . E . . C D . . H . . . E . . . . . G N V M V I I . . T . F epsilon-human

. . L K G T F A Q . . E . . C D . . H . . . E . . . . . G N V . V T V . . I . F gamma-humanG H H E A E I K P . A Q S . . T . H K I P V K Y L E F I . E . I I Q V . Q S K H myo-human

120 130 140

P A E F T P A V H A S L D K F L A S V S T V L T S K Y R - - - - - - alpha-humanG K . . . . P . Q . A Y Q . V V . G . A N A . A H . . H . . . . . . beta-human

G K . . . . Q M Q . A Y Q . V V . G . A N A . A H . . H . . . . . . delta-humanG K . . . . E . Q . A W Q . L V S A . A I A . A H . . H . . . . . . epsilon-humanG K . . . . E . Q . . W Q . M V T A . A S A . S . R . H . . . . . . gamma-human

. G D . G A D A Q G A M N . A . E L F R K D M A . N . K E L G F Q G myo-human

15

Human globins: uncorrected pairwise distances

Distances: between protein sequences. Calculated over: 1 to 154 Below diagonal: observed number of differences Above diagonal: number of differences per 100 amino acids

alpha beta delta eps gamma myo

alpha ---- 55 55 60 57 74 beta 82 ---- 7 25 27 75 delta 82 10 ---- 27 29 74

Eps 89 35 39 ---- 20 77

gamma 85 39 42 29 ---- 76 myo 116 117 116 119 118 ----

16

Human globinsCorrected pairwise distances

Distances: between protein sequences. Calculated over: 1 to 141 Below diagonal: observed number of differences Above diagonal: estimated number of substitutions per 100 amino acids Correction method: Jukes-Cantor

alpha beta delta epsil gamma myo

alpha ---- 281 281 281 313 208 beta 82 ---- 7 30 31 1000 delta 82 10 ---- 34 33 470

epsil 89 35 39 ---- 21 402

gamma 85 39 42 29 ---- 470 myo 116 117 116 119 118 ----

17

Neighbor-joining tree for globins

epsilon-human

alpha-human

myo-human

beta-humandelta-human

gamma-human

18

Neighbor-joining tree for globins (alternate form)

gamma-human

epsilon-human

alpha-human

myo-human

beta-human

delta-human

19

Why multiple alignment?

The simultaneous alignment of a number of DNA or protein sequences is one of the commonest tasks in bioinformatics.

Useful for:

phylogenetic analysis (inferring a tree, estimating rates of substitution, etc.)

detection of homology between a newly sequenced gene and an existing gene family

prediction of protein structure

demonstration of homology in multigene families

determination of a consensus sequence (e.g., in assembly)

20

10 20 30 40 50 60 . . . . . .Hbb_Human.pep --------VHLTPEEKSAVTALWGKVN--VDEVGGEALGRLLVVYPWTQRFFESFGDLSTHbb_Horse.pep --------VQLSGEEKAAVLALWDKVN--EEEVGGEALGRLLVVYPWTQRFFDSFGDLSNHba_Human.pep ---------VLSPADKTNVKAAWGKVGAHAGEYGAEALERMFLSFPTTKTYFPHFDLS--Hba_Horse.pep ---------VLSAADKTNVKAAWSKVGGHAGEYGAEALERMFLGFPTTKTYFPHFDLS--Myg_Phyca.pep ---------VLSEGEWQLVLHVWAKVEADVAGHGQDILIRLFKSHPETLEKFDRFKHLKTGlb5_Petma.pep PIVDTGSVAPLSAAEKTKIRSAWAPVYSTYETSGVDILVKFFTSTPAAQEFFPKFKGLTTLgb2_Luplu.pep --------GALTESQAALVKSSWEEFNANIPKHTHRFFILVLEIAPAAKDLFSFLKGTSE *. . * * . *

Hbb_Human.pep PDAVMGNPKVKAHGKKVLGAFSDGLAHLD-----NLKGTFATLSELHCDKLHVDPENFRLHbb_Horse.pep PGAVMGNPKVKAHGKKVLHSFGEGVHHLD-----NLKGTFAALSELHCDKLHVDPENFRLHba_Human.pep ----HGSAQVKGHGKKVADALTNAVAHVD-----DMPNALSALSDLHAHKLRVDPVNFKLHba_Horse.pep ----HGSAQVKAHGKKVGDALTLAVGHLD-----DLPGALSNLSDLHAHKLRVDPVNFKLMyg_Phyca.pep EAEMKASEDLKKHGVTVLTALGAILKKKG-----HHEAELKPLAQSHATKHKIPIKYLEFGlb5_Petma.pep ADQLKKSADVRWHAERIINAVNDAVASMDDT--EKMSMKLRDLSGKHAKSFQVDPQYFKVLgb2_Luplu.pep VP--QNNPELQAHAGKVFKLVYEAAIQLQVTGVVVTDATLKNLGSVHVSKG-VADAHFPV .. * . * * .

Hbb_Human.pep LGNVLVCVLAHHFGKEFTPPVQAAYQKVVAGVANALAHKYH------Hbb_Horse.pep LGNVLVVVLARHFGKDFTPELQASYQKVVAGVANALAHKYH------Hba_Human.pep LSHCLLVTLAAHLPAEFTPAVHASLDKFLASVSTVLTSKYR------Hba_Horse.pep LSHCLLSTLAVHLPNDFTPAVHASLDKFLSSVSTVLTSKYR------Myg_Phyca.pep ISEAIIHVLHSRHPGDFGADAQGAMNKALELFRKDIAAKYKELGYQGGlb5_Petma.pep LAAVIADTVAAG---------DAGFEKLMSMICILLRSAY-------Lgb2_Luplu.pep VKEAILKTIKEVVGAKWSEELNSAWTIAYDELAIVIKKEMNDAA--- . . . .

A multiple alignment

21

Extending the pairwisealignment algorithms

• Generally not feasible for more than a small number of sequences (~5), as the necessary computer time and space quickly becomes prohibitive. Computational time grows as Nm, where m = number of sequences. For example, for 100 residues from 5 species, 1005 = 10,000,000,000 (i.e., the equivalent of two sequences each 100,000 residues in length.)

• Nor is it wholly desirable to reduce multiple alignment to a similar mathematical problem to that tackled by pairwise alignment algorithms. Two issues which are important in discussions of multiple alignment are:

the treatment of gaps: position-specific and/or residue-specific gap penalties are both desirable and feasible, and

the phylogenetic relationship between the sequences (which must exist if they are alignable): it should be exploited.

22

Progressive alignment

Up until about 1987, multiple alignments would typically be constructed manually, although a few computer methods did exist. Around that time, algorithms based on the idea of progressive alignment appeared. In this approach, a pairwise alignment algorithm is used iteratively, first to align the most closely related pair of sequences, then the next most similar one to that pair, and so on.

The rule “once a gap, always a gap” was implemented, on the grounds that the positions and lengths of gaps introduced between more similar pairs of sequences should not be affected by more distantly related ones.

23

Multiple alignment in 2002

The most widely used progressive alignment algorithm is currently CLUSTAL W. However, there are a number of more specialized procedures based on quite different principles, including the use of hidden Markov models built for protein families. A relatively new and promising approach uses Markov chain Monte Carlo methods to sample alignments according to certain probabilistic procedures and, by moving randomly around in the huge space of possible alignments, to find good alignments.

24

CLUSTAL W

The three basic steps in the CLUSTAL W approach are shared by all progressive alignment algorithms:

A. Calculate a matrix of pairwise distances based on pairwise alignments between the sequences

B. Use the result of A to build a guide tree, which is an inferred phylogeny for the sequences

C. Use the tree from B to guide the progressive alignment of the sequences

25

Calculating the pairwise distances (A)

A pair of sequences is aligned by the usual dynamic programming algorithm, and then a similarity or distance measure for the pair is calculated using the aligned portion (gaps excluded) - for example, percent identity.

CLUSTAL W does not correct these distances for multiple substitutions (e.g., by the Jukes-Cantor formula), although other programs do, and it is sometimes an option in different versions of the program.

26

Globin example

DISTANCES between protein sequences:

Calculated over: 1 to 167 Correction method: Simple distance (no corrections) Distances are: observed number of substitutions per 100 amino acidsSymmatrix version 1Number of matrices: 1

//Matrix 1, dimension: 7

Key for column and row indices:

1 hba_human 2 hba_horse 3 hbb_human 4 hbb_horse 5 glb5_petma 6 myg_phyca 7 lgb2_luplu

Matrix 1: Part 1

1 2 3 4 5 6 7________________________________________________________________________________ ..| 1 | 0.00 12.06 54.68 55.40 64.12 71.74 83.57| 2 | 0.00 55.40 53.96 64.89 72.46 82.86| 3 | 0.00 16.44 74.26 73.94 82.52| 4 | 0.00 75.74 73.94 81.12| 5 | 0.00 75.91 82.61| 6 | 0.00 80.95| 7 | 0.00

27

Building the guide tree (B)

• There are many ways of building a tree from a matrix of pairwise distances. CLUSTAL W uses the neighbour-joining (NJ) method, which is the most favoured approach these days. Earlier versions of CLUSTAL used the unweighted pair group method using arithmetic averages (UPGMA), and this is still used in some programs.

• A root of the tree is then determined by the so-called mid-point method (giving equal means for the branch lengths on either side of the root).

• The W in CLUSTAL W stands for Weights, an important feature of this program. These are calculated in a straightforward way. They correct for unequal sampling at different evolutionary distances.

28

hba_human

hba_horse

hbb_humanhbb_horse

glb5_petma

myg_phyca

lgb2_luplu

NJ globin tree

29

hbb human: 0.221

hbb horse: 0.225

hba human: 0.194

hba horse: 0.203

myg phyca: 0.411

glb5 petma: 0.398

lgb2 luplu: 0.442

.081

.084

.055

.065

.226

.219

.061

.015

.062 .398

.389

.442

Tree, distances, and weights Thompson et al. (1994)

30

Progressive alignment (C)

The basic idea is to use a series of pairwise alignments to align larger and larger groups of sequences, following the branching order of the guide tree. We proceed from the tips of the rooted tree towards the root.

In our globin example, we align in the following order:a) human and horse -globin;b) human and horse -globin;c) the two -globins and the two -globins;d) myoglobin and the haemoglobins;e) cyanohaemoglobin and the combined haemoglobin,

myoglobin group;f) leghaemoglobin and the rest.

31

Progressive alignment (C, 2)

At each stage a full dynamic programming algorithm is used, with a residue scoring matrix (e.g., a PAM or a BLOSUM matrix) and gap opening and extension penalties.

Each step consists of aligning two existing alignments. Scores at a position are averages of all pairwise scores for residues in the two sets of sequences using matrices with only positive values. Gap vs. residue scores zero. Sequence weights are used at this stage. See next slide.

Gaps that are present in older alignments remain fixed. New gaps introduced at each stage initially get full opening and extension penalties, even if inside old gap positions. This gets modified.

32

Scoring an alignment of two partial alignments

1 peeksavtal2 geekaavlal3 padktnvkaa4 aadktnvkaa

5 egewqlvlhv6 aaektkirsa

Sequence weightsw1,...,w6

Score: 1

8M(t, v)w1w5 + M(t,i)w1w6 + ... + M(k,i)w4w6[ ]

33

Progressive alignment (C) - gaps

CLUSTAL W has quite a sophisticated treatment of gaps, incorporating into opening and extension penalties a dependence on a) weight matrix, b) sequence similarity, c) sequence length, d) difference in sequence length, e) position of gaps (see figure), f) residues at gaps.

Regarding e) and f), the motivation is as follows: if one knew the positions of all secondary structure elements (-helices, -strands) in all or some of the sequences, one could increase the gap penalties inside and decrease outside them, forcing gaps to occur most often in loop regions, which is what is observed in alignments of sequences with known 3-D structure.

For further details, see Thompson et al., NAR 1994, 22:4673 or Methods in Enz. 1996, 266:article 22.

34

Position and residue -specific gap opening penalties

HLTPEEKSAVTALWGKVN--VDEVGGEALGRLLVVYPWTQRFFESFGDLQLSGEEKAAVLALWDKVN--EEEVGGEALGRLLVVYPWTQRFFDSFGDLVLSPADKTNVKAAWGKVGAHAGEYGAEALERMFLSFPTTKTYFPHFDLSVLSAADKTNVKAAWSKVGGHAGEYGAEALERMFLGFPTTKTYFPHFDLS

35

10 20 30 40 50 60 . . . . . .Hbb_Human.pep --------VHLTPEEKSAVTALWGKVN--VDEVGGEALGRLLVVYPWTQRFFESFGDLSTHbb_Horse.pep --------VQLSGEEKAAVLALWDKVN--EEEVGGEALGRLLVVYPWTQRFFDSFGDLSNHba_Human.pep ---------VLSPADKTNVKAAWGKVGAHAGEYGAEALERMFLSFPTTKTYFPHFDLS--Hba_Horse.pep ---------VLSAADKTNVKAAWSKVGGHAGEYGAEALERMFLGFPTTKTYFPHFDLS--Myg_Phyca.pep ---------VLSEGEWQLVLHVWAKVEADVAGHGQDILIRLFKSHPETLEKFDRFKHLKTGlb5_Petma.pep PIVDTGSVAPLSAAEKTKIRSAWAPVYSTYETSGVDILVKFFTSTPAAQEFFPKFKGLTTLgb2_Luplu.pep --------GALTESQAALVKSSWEEFNANIPKHTHRFFILVLEIAPAAKDLFSFLKGTSE *. . * * . *

Hbb_Human.pep PDAVMGNPKVKAHGKKVLGAFSDGLAHLD-----NLKGTFATLSELHCDKLHVDPENFRLHbb_Horse.pep PGAVMGNPKVKAHGKKVLHSFGEGVHHLD-----NLKGTFAALSELHCDKLHVDPENFRLHba_Human.pep ----HGSAQVKGHGKKVADALTNAVAHVD-----DMPNALSALSDLHAHKLRVDPVNFKLHba_Horse.pep ----HGSAQVKAHGKKVGDALTLAVGHLD-----DLPGALSNLSDLHAHKLRVDPVNFKLMyg_Phyca.pep EAEMKASEDLKKHGVTVLTALGAILKKKG-----HHEAELKPLAQSHATKHKIPIKYLEFGlb5_Petma.pep ADQLKKSADVRWHAERIINAVNDAVASMDDT--EKMSMKLRDLSGKHAKSFQVDPQYFKVLgb2_Luplu.pep VP--QNNPELQAHAGKVFKLVYEAAIQLQVTGVVVTDATLKNLGSVHVSKG-VADAHFPV .. * . * * .

Hbb_Human.pep LGNVLVCVLAHHFGKEFTPPVQAAYQKVVAGVANALAHKYH------Hbb_Horse.pep LGNVLVVVLARHFGKDFTPELQASYQKVVAGVANALAHKYH------Hba_Human.pep LSHCLLVTLAAHLPAEFTPAVHASLDKFLASVSTVLTSKYR------Hba_Horse.pep LSHCLLSTLAVHLPNDFTPAVHASLDKFLSSVSTVLTSKYR------Myg_Phyca.pep ISEAIIHVLHSRHPGDFGADAQGAMNKALELFRKDIAAKYKELGYQGGlb5_Petma.pep LAAVIADTVAAG---------DAGFEKLMSMICILLRSAY-------Lgb2_Luplu.pep VKEAILKTIKEVVGAKWSEELNSAWTIAYDELAIVIKKEMNDAA--- . . . .

7 -helices

Final CLUSTALW alignment (using eclustalw)

36

Alignment using Hidden Markov models

There are now many HMMs for protein families such as globins, and these models can be used to infer alignments of new globin sequences to other members of the family.

Such models can also be used to determine whether a given sequence is or is not a member of a specified family.

37

HMM Model for a Protein Domain

38

Web-based multiple sequence alignment

• ClustalW www2.ebi.ac.uk/clustalw/ dot.imgen.bcm.tmc.edu:9331/multi-align/Options/clustalw.html www.clustalw.genome.ad.jp/ bioweb.pasteur.fr/intro-uk.html pbil.ibcp.fr transfac.gbf.de/programs.html www.bionavigator.com

• PileUp helix.nih.gov/newhelix www.hgmp.mrc.ac.uk/ bcf.arl.arizona.edu/gcg.html www.bionavigator.com

• Dialign genomatix.gsf.de/ bibiserv.techfak.uni-bielefeld.de/ bioweb.pasteur.fr/intro-uk.html www.hgmp.mrc.ac.uk/

• Match-box www.fundp.ac.be/sciences/biologie/bms/matchbox_submit.html

• For reviews: G. J. Gaskell, BioTechniques 2000, 29:60, andwww.techfak.uni-bielefeld.de/bcd/Curric/MulAli/welcome.html

39

Comparing multiple sequence alignment programs

Even below the 10-20% identity twilight zone, the best programs correctly align 47% of residues on average

Iterative algorithms are superior, but with a large trade-off in use of computational resources

Global generally performs better than local

No single ‘best’ program exists

For reviews, see:

P. Briffeuil et al., Bioinformatics 1998, 14:357

J. D. Thompson et al., NAR 1999, 27:2682

40

Multiple sequence alignment editors

• EditSeq/MegAlign - Lasergene - Mac or MS-Windows• DNA Strider - Macintosh• Seq-Al - Macintosh• ASAD - Excel - Macintosh or MS-Windows• BioEdit - MS-Windows• Genedoc - MS-Windows• SeqPup - Mac. MS-Windows, X-Windows• For a review of these:

http://www.wehi.edu.au/bioweb/KeithsStuff/seqeditors.html